SteveM wrote:I am not sure any 'probability calculation' is applicable here, with too little material for a statistical analasys of any significance.
Well, you couldn't find more data at that moment (2003/04), and in any other imaginable research situation it would be similar - it never will be enough data.
But even the stupid researcher can identify the hole ...
... and as even the stupid researcher has a little bit time and can describe the situation (" there is a rather unusual big hole") and he might search for ways to calculate, how rare such a big hole (
6 empty years in a row of 22) between the first and the last entry would be in probability calculation (in which everything is accidental):
6/22 = 8/11
20 possibilities, how the hole can occur (between the first and the last year, which both must have a content); 1st is 43-48, 2nd 44-49 etc. and the last is 56-61.
So one can calculate the probability for 43-48 and multiply the result with 20 to calculate the probability for all holes with .
43-48 is that, what shall not be hit, so I have to calculate the other side (16/22 = 8/11).
((8/11)^27)*20
Well, I hope this is right ... the finish button leads to "0.00368856248 ..", which is roughly "0,37%" or a chance of "1 : 271".
Actually this result is higher, as it should be, cause there are solutions with 7 or more empty places in a sequence and this reduces the value "0.00368856248" and naturally increases the 271 in 1 : 271. And my method (*20) isn't correct, it should be less ... but I leave this problem, as it is, the things start to become too complicated with this, at least for me.
The appearance of six empty places (or more) in such a row is rare, if you only ask normal distribution in a manner, as if all years have the same chance to have Trionfi notes. In the normal historical situation they shouldn't have the same chance, logically. In the first years the number of existing games should be much lower than in the later years, less decks should produce less records than more decks. On the other side there is a "novelty factor". A "new type of deck" has more chances to be recorded in a historical document than an item, which already is a usual and common object.
A pause of a longer time in the first years of a new product should be a relative common feature (in spite of the rare factor of 1:271, as above shown in our research example). The pause simply signals, that the deck development is (likely) in a state of "normal early distribution".
A further historical factor in our calculations is the appearance of prohibitions. New inventions might mean , that some social forces don't agree with the new product, and attempt to regulate their society in this point. So we meet also a punishment for playing with Trionfi cards (1444), and later a series of allowances (since 1450) for the game in the documents.
Well ... we discussed this all repeatedly. And we have asimilar stupid (but normal) hole in the discussions about the
begin of the playing card development (1367 Bern and 1377 Florence).
That it conflicts with what we can imagine as there being a conflation of the theological virtues with star - moon - sun at a later date is no argument, perhaps what we can imagine is just that, a product of our imagination, a mere fantasy. As there being no record for a deck of cards being made for a marriage at this time, same applies to other decks as well, for which a marriage dating is argued.
We have simply the fact, that Cary-Yale included the theological virtues, and that we don't have sun-moon-star in the Cary-Yale. In the later Trionfi decks we have no theological virtues (beside Mantegna Tarocchi series and Minchiate), but we have sun-moon-star instead (Charles VI, PMB 2, Este cards). That's simply an observation and not imagination and not fantasy. And naturally we search for explanations for the observable changes.